"Communication on the Paper “A Reference-Dependent Regret Model for Deterministic Tradeoff Studies”"
Journal of Systems Engineering,
Vol. 11, No. 4, pp. 360-364, 2008.
Xiaoting Wang, Evangelos Triantaphyllou, and Edouard Kujawski
This communication focuses on a fundamental problem related to the recently introduced Reference-Dependent Regret Model
(RDRM) [Kujawski, 2005] for deterministic multi-criteria decision making. In [Kujawski, 2005]
it was asserted that the RDRM model satisfies three properties. The first of these properties, referred to
as the “independence of dominated alternatives”, seems to be an intuitive one. According to this property,
the RDRM model preserves the ranking of two alternatives A i and A j
with ranking A i > A j when a new alternative dominated by A i
is introduced or an old alternative dominated by A j is dropped.
In this communication it is demonstrated algebraically and also by means of a numerical example
that the RDRM model may fail to satisfy this property. The implication is that when the concepts of
regret and/or rejoicing are considered and defined in terms of all the available alternatives
in accordance with the RDRM, adding or dropping a dominated alternative can change the ranking of the alternatives
and violate the independence of dominated alternatives property.